Draw two triangles that are similar. Similar triangles have the exact same angle measurements on all three angles, but they can have different lengths of sides.
On your triangles, mark the three corners ABC on one and DEF on the other, make sure that you A on the first is in the same place as D on the other, since their angles are both 60 degrees. Then mark your other corners and write the measurements of the sides that are given. Once you have your triangles labeled, use the pathagorean theorum to solve for your unknown sides. Remember that c^2 is always your hypotenuse!! Hope that helps! Good luck!

Similar Triangles

How should I draw a triangle of ABC and DEF from these values ? If AB and DF, how can I get ABC ? And what unknown sides ? Im confused :S

I'm sorry, but this question can't be correct. The information given is contradictory.

See the attached diagram.

Bear in mind that you can only use Pythagoras' Theorem when you know that the triangle is right-angled - and you don't know this here.

You could now find the length of the side BC using the Cosine Rule: . Then find another angle using the Sine Rule, and the third angle using angle sum = 180 degrees.

Looking at the triangle DEF, you can find the angle E using the Sine Rule, and hence the other angle and sides.

But, given those measurements, the triangles are not then similar - the angles of one triangle have to be the same as the angles of the other for them to be similar, and the sides in the same ratio.

Originally Posted by Serialkisser

Another question I have:

2 sides of one triangle are in proportion to 2 sides of a second triangle. One angle - not the contained angle - is equal to another angle - not the contained angle - in the second triangle.

Is this a similar triangle ? If not why.

No, the equal angles must be opposite to the corresponding sides, and you cannot be certain that this is so.

For example, if the triangles are ABC and DEF, and we know that the side BC corresponds to side DF, and AC corresponds to DE - in other words the ratios are equal, BC : DF = AC : DE - then the angles opposite these pairs of corresponding sides must be equal: A = E and B = F. And you cannot be sure that this is so from the information given.

They haven't learned any trig functions in this class yet, so I didn't see any other way to go about it. It does seem that there is info missing. I saw that 60 degrees and figured that maybe it was just a 30, 60, 90 triangle.. Did you change any part of that question? Is it worded exactly as it is in your homework?